SOLUTION: A sound whispered at one focus of a whispering gallery can be heard at the other focus. The figure at the top of the next column shows a whispering gallery whose cross section is a

Question 1107642: A sound whispered at one focus of a whispering gallery can be heard at the other focus. The figure at the top of the next column shows a whispering gallery whose cross section is a semielliptical arch with a height of 24 feet and a width of 80 feet. How far from the room�s center should two people stand so that they can whisper back and forth and be heard?

Answer by ikleyn(52887) (Show Source): You can put this solution on YOUR website!
.

The ellipse they are talking about, has the major axis of 80 ft long, so the major semi-axis is 40 ft.


It also has the minor semi-axis of 24 ft.


The people should stand at the focuses of this ellipse.


The focuses are remoted from the center of the room for the distance of  =  = 32 ft.

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About ellipses and their focal properties see the lessons
    - Ellipse definition, canonical equation, characteristic points and elements
    - Ellipse focal property
    - Tangent lines and normal vectors to a circle
    - Tangent lines and normal vectors to an ellipse
    - Optical property of an ellipse
    - Optical property of an ellipse revisited
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic
"Conic sections: Ellipses. Definition, major elements and properties. Solved problems".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

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